Liebermann, D. G., Biess, A., Friedman, J., Gielen, C. C. A. M., & Flash, T. (2006). Intrinsic joint kinematic planning. I: reassessing the Listing's law constraint in the control of three-dimensional arm movements. Exp Brain Res, 171(2), 139–154.
Abstract: This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing's law, can account for the geometric features of three-dimensional arm movements. In principle, if the arm joints follow a Listing's constraint, the hand paths may be predicted. Four individuals performed 'extended arm', 'radial', 'frontal plane', and 'random mixed' movements to visual targets to test Listing's law assumption. Three-dimensional rotation vectors of the upper arm and forearm were calculated from three-dimensional marker data. Data fitting techniques were used to test Donders' and Listing's laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a second-order equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between approximately 1.7 degrees and 4.7 degrees for the rotation vectors of the upper arm segment and approximately 2.6 degrees and 7.5 degrees for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a two-dimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing's law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during radial reaching movements.
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Liebermann, D. G., Berman, S., Weiss, P. L. T., & Levin, M. F. (2012). Kinematics of reaching movements in a 2-d virtual environment in adults with and without stroke. IEEE Trans Neural Syst Rehabil Eng, 20(6), 778–787.
Abstract: Virtual reality environments are increasingly being used for upper limb rehabilitation in poststroke patients. Our goal was to determine if arm reaching movements made in a 2-D video-capture virtual reality environment are similar to those made in a comparable physical environment. We compared arm and trunk kinematics for reaches made with the right, dominant arm to three targets (14 trials per target) in both environments by 16 adults with right poststroke hemiparesis and by eight healthy age-matched controls. Movement kinematics were recorded with a three-camera optoelectronic system at 100 samples/s. Reaching movements made by both control and stroke subjects were affected by viewing the targets in the video-capture 2-D virtual environment. Movements were slower, shorter, less straight, less accurate and involved smaller ranges of shoulder and elbow joint excursions for target reaches in the virtual environment compared to the physical environment in all subjects. Thus, there was a decrease in the overall movement quality for movements made in the 2-D virtual environment. This suggests that 2-D video-capture virtual reality environments should be used with caution when the goal of the rehabilitation program is to improve the quality of movement patterns of the upper limb.
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Biess, A., Flash, T., & Liebermann, D. G. (2011). Riemannian geometric approach to human arm dynamics, movement optimization, and invariance. Phys Rev E Stat Nonlin Soft Matter Phys, 83(3 Pt 1), 031927.
Abstract: We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparameterized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm's configuration space may provide insights into the emerging properties of the movements generated by the motor system.
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Liebermann, D. G., Levin, M. F., McIntyre, J., Weiss, P. L., & Berman, S. (2010). Arm path fragmentation and spatiotemporal features of hand reaching in healthy subjects and stroke patients. Conf Proc IEEE Eng Med Biol Soc, 2010, 5242–5245.
Abstract: Arm motion in healthy humans is characterized by smooth and relatively short paths. The current study focused on 3D reaching in stroke patients. Sixteen right-hemiparetic stroke patients and 8 healthy adults performed 42 reaching movements towards 3 visual targets located at an extended arm distance. Performance was assessed in terms of spatial and temporal features of the movement; i.e., hand path, arm posture and smoothness. Differences between groups and within subjects were hypothesized for spatial and temporal aspects of reaching under the assumption that both are independent. As expected, upper limb motion of patients was characterized by longer and jerkier hand paths and slower speeds. Assessment of the number of sub-movements within each movement did not clearly discriminate between groups. Principal component analyses revealed specific clusters of either spatial or temporal measures, which accounted for a large proportion of the variance in patients but not in healthy controls. These findings support the notion of a separation between spatial and temporal features of movement. Stroke patients may fail to integrate the two aspects when executing reaching movements towards visual targets.
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Roijezon, U., Djupsjobacka, M., Bjorklund, M., Hager-Ross, C., Grip, H., & Liebermann, D. G. (2010). Kinematics of fast cervical rotations in persons with chronic neck pain: a cross-sectional and reliability study. BMC Musculoskelet Disord, 11, 222.
Abstract: BACKGROUND: Assessment of sensorimotor function is useful for classification and treatment evaluation of neck pain disorders. Several studies have investigated various aspects of cervical motor functions. Most of these have involved slow or self-paced movements, while few have investigated fast cervical movements. Moreover, the reliability of assessment of fast cervical axial rotation has, to our knowledge, not been evaluated before. METHODS: Cervical kinematics was assessed during fast axial head rotations in 118 women with chronic nonspecific neck pain (NS) and compared to 49 healthy controls (CON). The relationship between cervical kinematics and symptoms, self-rated functioning and fear of movement was evaluated in the NS group. A sub-sample of 16 NS and 16 CON was re-tested after one week to assess the reliability of kinematic variables. Six cervical kinematic variables were calculated: peak speed, range of movement, conjunct movements and three variables related to the shape of the speed profile. RESULTS: Together, peak speed and conjunct movements had a sensitivity of 76% and a specificity of 78% in discriminating between NS and CON, of which the major part could be attributed to peak speed (NS: 226 +/- 88 degrees /s and CON: 348 +/- 92 degrees /s, p < 0.01). Peak speed was slower in NS compared to healthy controls and even slower in NS with comorbidity of low-back pain. Associations were found between reduced peak speed and self-rated difficulties with running, performing head movements, car driving, sleeping and pain. Peak speed showed reasonably high reliability, while the reliability for conjunct movements was poor. CONCLUSIONS: Peak speed of fast cervical axial rotations is reduced in people with chronic neck pain, and even further reduced in subjects with concomitant low back pain. Fast cervical rotation test seems to be a reliable and valid tool for assessment of neck pain disorders on group level, while a rather large between subject variation and overlap between groups calls for caution in the interpretation of individual assessments.
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